M1827799 Mersenne number exponent details

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁶⁸	32.6102	69.1176%	2861526	182779900	0.9962	8.3332%	33.6064	71.6911%	2.5735%
PrimeNet	2⁵⁷	0.0105	63.1579%	8000	150000	0.0012	2.8785%	0.0117	64.2184%	1.0605%
GPU72	2⁶¹	0.1681	65.5738%	9000	140000	0.0013	1.5942%	0.1693	66.1226%	0.5488%
Difference	+7	+32.4421	+3.5439%	+2852526	+182639900	+0.9949	+6.7390%	+33.4370	+5.5685%	+5.5685%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1827799	10492021511740170245953	23	73.152	2870124535504224 2⁵ × 3² × 20143 × 494748061	2019-11-24	20143	494748061	2,057.8	2.1219	3.9603

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2011-12-31T14:27:00	markr	tiny	275000	6000000		-		-	-	0.046	-	-	3.526%
2015-10-06T21:30:11	Bruno Victal	5820K-linux	500000	15000000	12	-		-	-	0.101	-	-	4.599%
2016-08-23T15:10:32	Jocelyn Larouche	Manual testing	500000	30000000	12	-		-	-	0.166	-	-	5.211%
2016-10-07T05:52:36	Jocelyn Larouche	low 4M	500000	36000000	6	-		-	-	0.191	-	-	5.374%
2016-10-27T15:20:23	Jocelyn Larouche	low 4M	798600	798600		-		-	-	0.063	-	-	2.159%
2016-10-29T20:53:42	Jocelyn Larouche	low 4M	958320	958320		-		-	-	0.075	-	-	2.321%
2017-03-17T06:02:32	Jocelyn Larouche	low 4M	1379980	13799800	12	-		-	-	0.162	-	-	5.017%
2017-03-21T00:47:12	Jocelyn Larouche	low 4M	1655976	16559760	12	-		-	-	0.194	-	-	5.283%
2017-03-29T03:10:18	Jocelyn Larouche	low 4M	1987171	19871710	12	-		-	-	0.233	-	-	5.555%
2017-03-31T06:29:11	Jocelyn Larouche	low 4M	2384605	23846050	12	-		-	-	0.280	-	-	5.833%
2017-05-22T21:10:26	Jocelyn Larouche	low 4M	2861526	28615260	12	-		-	-	0.335	-	-	6.117%
2018-02-11T11:28:51	Jocelyn Larouche	low 4M	2861526	57230520	12	-		-	-	0.458	-	-	6.941%
2018-03-01T12:55:02	Jocelyn Larouche	low 4M	2861526	114461040	12	-		-	-	0.703	-	-	7.771%
2018-05-02T16:53:29	Jocelyn Larouche	low 4M	2861526	182779900	12	-		-	-	0.996	-	-	8.333%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2003-01-16T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.021	-	-
2016-02-23T16:28:54	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.063	-	-
2010-04-11T14:32:00	Architects Cubed	Manual testing	2⁶⁰	2⁶¹		-	-	0.084	-	-
2016-02-23T16:28:54	Mark Rose	Manual testing	2⁶¹	2⁶²		-	-	0.168	-	-
2011-03-08T05:14:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.873	-	-
2016-02-23T16:28:54	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.537	-	-
2015-04-25T21:24:00	snme2pm1	Manual testing	2⁶³	2⁶⁴		-	-	1.074	-	-
2015-04-25T21:24:00	snme2pm1	Manual testing	2⁶⁴	2⁶⁵		-	-	2.044	-	-
2015-09-04T17:59:00	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	4.088	-	-
2018-04-23T13:17:24	TJAOI	Manual testing	2⁶⁶	2⁶⁷		-	-	8.177	-	-
2019-06-24T09:36:03	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	16.35	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	19.057 GHz-days
Estimated T-Level:	24.482

Digits	B1	Curves	Complete	FacMiss
20	11000	251 / 100	2.510	8.025%
25	50000	251 / 280	0.896	40.737%

New Calculation Method

Total ECM effort:	19.057 GHz-days
Estimated T-Level:	24.482

Digits	B1	Complete	FacMiss
20	11000	8.533	0.020%
25	50000	0.773	46.170%
30	250000	0.048	95.333%
35	1000000	0.002	99.781%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		54	3.729
50000	5000000	10492021511740170245953	1	0.069
50000	6600000		196	15.26

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-10-06T15:41:00	Scott Kurowski	HomeOffice	50000	5000000						3	0.207
2009-07-17T03:48:00	James Hintz	15_071509	50000	5000000						3	0.207
2011-01-06T04:32:00	c10ck3r	aleman	50000	5000000						3	0.207
2012-05-16T04:38:00	Chang Chia-Tche	sekhmet	50000	5000000						3	0.207
2013-08-15T12:48:00	OS1	L3	50000	5000000						3	0.207
2014-05-01T10:30:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.207
2014-10-10T16:49:00	mikr	MSI	50000	5000000						12	0.829
2016-05-28T04:46:25	Bruce	DESK3	50000	5000000						3	0.207
2016-08-31T23:40:11	Bruce	DESK3	50000	5000000						3	0.207
2016-11-10T20:42:33	Chang Chia-Tche	exbpc13	50000	5000000						3	0.207
2017-01-09T06:22:29	Chang Chia-Tche	exbpc13	50000	5000000						3	0.207
2017-04-29T14:38:46	ANONYMOUS	Worker	50000	5000000						3	0.207
2017-12-01T22:02:09	Bruce	DESK3	50000	5000000						3	0.207
2018-02-05T13:26:58	Bruce	DESK3	50000	5000000						3	0.207
2019-11-23T02:51:06	Claude Portenier	Petit-Idiot	50000	5000000						3	0.207
2019-11-24T19:12:15	Chang Chia-Tche	ex-ctcpc	50000	5000000	10492021511740170245953	73.152	1	2	5681674673095961	1	0.069
2021-04-16T16:25:03	TJAOI	Manual testing	50000	6600000						196	15.26

date	userid	compid	res64	spent (GHz-days)
1998-12-21T00:00:00	ANONYMOUS	v4_computers	8B85D765411F1AE7	0.099
2015-06-27T00:54:00	MadPoo	Manual testing	8B85D765411F1AE7	0.099

P-1 factor-bounds graph:

X = B1; Y = B2
size of marker relates to size of factor
mouse-over any factor marker (circle) to see additional info
mouse-over any stage bound text to see additional info

B1 = 2861526, B2 = 182779900 (P-1 stage 2)

B1 = 2861526, B2 = 114461040 (P-1 stage 2)

B1 = 2861526, B2 = 57230520 (P-1 stage 2)

B1 = 2861526, B2 = 28615260 (P-1 stage 2)

B1 = 2384605, B2 = 23846050 (P-1 stage 2)

B1 = 1987171, B2 = 19871710 (P-1 stage 2)

B1 = 2861526 (P-1 stage 1)

B1 = 1655976, B2 = 16559760 (P-1 stage 2)

B1 = 500000, B2 = 36000000 (P-1 stage 2)

B1 = 2384605 (P-1 stage 1)

B1 = 500000, B2 = 30000000 (P-1 stage 2)

B1 = 1379980, B2 = 13799800 (P-1 stage 2)

B1 = 1987171 (P-1 stage 1)

B1 = 1655976 (P-1 stage 1)

B1 = 1379980 (P-1 stage 1)

B1 = 500000, B2 = 15000000 (P-1 stage 2)

B1 = 958320 (P-1 stage 1)

B1 = 798600 (P-1 stage 1)

B1 = 275000, B2 = 6000000 (P-1 stage 2)

B1 = 500000 (P-1 stage 1)

B1 = 275000 (P-1 stage 1)

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0M	<	10¹⁰	All tracked exponents
0M	<	2³²	GPU TF range
0M	<	1000M	PrimeNet range
0M	<	193M	low-PrimeNet, low-res
0M	<	385M	low-PrimeNet, high-res
50M	<	146M	PrimeNet wavefront